Q & A: conservation of mechanical energy

Q:
Hi, I am confused with a couple questions for physics. The teacher didn't really do a good job of explaining, so I'm totally stumped. Can I just have a walk through of what I should do?1. A box moved up a ramp with an incline of 35� with a velocity of 20 m/s. How far will it travel up the ramp before it stops?2. A spring toy of mass 300g is compressed 5cm. It is then released a reaches a maximum height. If the spring constant is 2800 N/m, what is the maximum height the toy reaches? What is the speed of the toy when it hits the ground?3. A 5.0 kg ball is held at the top of a 325m tall building. If you set the zero point at the top of the building, what is the ball's potential energy? If the zero point is 100m above the ball's starting position what is the balls potential energy? If you set the zero point at ground level, what is the ball's velocity at the very bottom?
- Emily (age 15)
California, USA
A:

All of these questions are doable by setting initial total mechanical energy = final total mechanical energy.

And knowing that Potential energy due to gravity is mgh  mass times "g" times height above a reference level.

Potential energy in a spring is (1/2) k  d^2  where k = spring stiffness and d is the amount the spring is compressed or extended.

And Kinetic energy is (1/2) mass times speed^2

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Here's an example problem:  a 4 kg mass is placed on a 80 Newton/meter spring and compressed 30 cm = 0.3 meters.   Before it is released the system has energy (1/2) 80 (.3)^2 = 36 Joules.   After the spring releases it has no energy; all the energy is then in the mass's Kinetic energy = (1/2) M V^2.    We solve for V and get about 4.2 m/sec.    We can take this further and ask then (if the speed is straight upwards), how far does it go?   It should go to a height given by 36 Joules = mg h, so h is about 0.9 meters as the kinetic energy is converted to gravitational potential energy

Richard

p.s. For other readers considering asking for help with standard school problems, we do this very, very rarely. MW

(published on 03/07/2016)